1. What is the Length of Rectangle Given Perimeter and Circumradius Formula?

This formula calculates the length of a rectangle when you know its perimeter and circumradius. The circumradius is the radius of the circle that passes through all four vertices of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l \) — Length of the rectangle (m)
• \( P \) — Perimeter of the rectangle (m)
• \( r_c \) — Circumradius of the rectangle (m)

Explanation: This formula derives from the relationship between a rectangle's dimensions, its perimeter, and the circumradius of its circumscribed circle.

3. Importance of Rectangle Length Calculation

Details: Calculating the length of a rectangle from its perimeter and circumradius is useful in geometry problems, architectural design, and various engineering applications where these specific parameters are known.

4. Using the Calculator

Tips: Enter the perimeter and circumradius values in meters. Both values must be positive numbers. The calculator will compute the length of the rectangle.

5. Frequently Asked Questions (FAQ)

Q1: What is the circumradius of a rectangle?
A: The circumradius is the radius of the circle that passes through all four vertices of the rectangle. For a rectangle, it's half the length of the diagonal.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, this formula works for squares as well.

Q3: What if I get an error message?
A: The error "square root of negative number" means the input values don't form a valid rectangle. Check your measurements.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values. Rounding may occur in the displayed result.

Q5: Can I use different units?
A: Yes, as long as you use consistent units for all inputs, the result will be in the same unit.